Uranium-niobium alloys exhibit complex crystal phases and unique mechanical behaviors under various thermodynamic states and external loadings. However, the lack of accurate interatomic potentials hinders people’s understanding of the atomic-scale phase behaviors and dynamical processes in this important alloy. In recent years, the development of machine-learning-based force fields has provided a systematic way to generate accurate interatomic potentials on large and complex first-principle-based datasets. However, this crucial nuclear material has received limited attention from researchers in the field of machine-learning potentials.
In this work, based on our previous development of the neural-network potential training and evaluation framework, which we called NNAP, a new neural network potential is constructed for the uranium-niobium alloy system. We employ a combination of random structure search and active learning algorithms to enhance coverage of the chemical and structural space of the alloy system. Testing of the generated potential demonstrates high generalization performance and accuracy. The mean absolute errors in energy and force are 5.6 meV/atom and 0.095 eV/Å on the testing set, respectively. Further calculation results of crystal structure parameters, equation of state and phonon dispersions coincide well with the first-principle or experimental references.
Based on the newly trained potential, we investigated the atomic-scale evolution of the spinodal decomposition process in the U-Nb alloys. We show that the atom-swapping hybrid Monte Carlo can be a powerful tool to understand the thermodynamic evolution of the systems. By employ the atom-swapping hybrid Monte Carlo method, the potential energy reduce due to phase segregation is captured within 5000 steps, while no significant energy reduction is found after 3 ns MD simulation. Finally, we calculate the stress-strain curves under shear loading for different initial states. We found that the Nb precipitation generated strengthened phases in the alloy and significantly changed the deformation behavior of U-Nb alloys, where a disorder shear band emerges in the deformation path of the γ phase alloys. Our work lays a new foundation to understand the mechanical processes in this important alloy system.